Junior's sudden weight gain? He was always eating the amount he presently does, but due to his hyperactivity, he simply managed to burn off all of that weight. If he's now taking medication which caused his symptoms to diminish and stops him running around like he used too, he naturally put it on (or his medication has a side effect of weight gain).
Apparently confirmed, as Junior once mentioned his hyperactivity medication caused him to put on weight. A recent episode however suggested that the original hyperactive Slim!Junior was killed and his identity stolen by Fat!Junior, as part of a massive gambit to assassinate Tim, the head of a terrorist sleeper-cell!
Stewie calls Cleveland and Junior chocolate people in the pilot because he's a little kid who doesn't know that calling a black person "chocolate people" could be taken as offensive. So, why did Joe do the same? Easy — it's a joke on racial profiling because he's a cop.
Cleveland Jr knowing Spanish in "The Hangover: Part Tubbs" is less random when you remember he dated a Mexican girl the previous season.
On the episode "The Men in Me," Cleveland is declared the whitest black man in America. This explains why Brian (who was established to be racist against black people because of his father) never barked at him when he lived in Quahog. He thought of him as a white guy.
Cleveland's Dad referring to Rallo as black Stewie sounds like a Lampshade Hanging but he's more than likely met the Griffins before.
Why did Mr. Waterman pick Tim the Bear over Cleveland or Terry on "Like a Boss"? Because Mr. Waterman is such a racist that he'd pick a bear over a black man. As for why he didn't pick Terry, since he has a crush on him and sexually harasses him (with Terry not noticing or caring), it's possible that the FOX censors wouldn't let the writers get away with that.
On Donna's hatred of Phylicia Rashad: Rashad voices her mother. It's entirely possible that she subconsciously remembers her mother's voice, causing painful memories to bubble up when she hears it.
Justin Bieber is shown to be a robot, but the Family Guy episode "Lois Comes Out Of Her Shell" aired almost a year later and shows him to be human. Is this Rule of Funny or is the Family Guy continuity separate from its Spin-Off?
Maybe the Bieber robot was invented as a way for Justin Beiber to do two concerts at once? Or maybe it's a joke about how most celebrities today (musicians, mostly) might as well be robots as they have no personality and their talent is prefabricated by a lot of industry insiders)?
Why is Cleveland referred to as Freight Train's only son if he has a brother Broderick (the plastic surgeon from the Family Guy episode where Peter gets plastic surgery, and he also appeared on in a season 1 episode of The Cleveland Show) Is Broderick his half brother?
Bit part from twenty years ago, no one remembered.
Someone remembered since Broderick showed up on this show.
Well, it was shown in a cutaway that Freight Train had multiple illegitimate children (all over the world, to be exact) so it's possible that he may not be aware of Broderick but Cleveland and Cookie are or Broderick might be a half-brother that Cookie may have had from a previous relationship.